where it has the same distance from A and B:

- Drag the point C across the drawing's surface and...
- ...watch the values of the two distance measures:

When you succeed to move the point C in such a way that its distance from point A equals the distance from point B, then you can make the point C draw a trace:

- chose the tool "Record a locus line",
- click the point C,
- then grip it with the pair of pliers....
- ...and drag it over the surface.

After having recognized this, you can construct this "curve": use the tool "Line through 2 points". Now you must assure that C runs always on this line. You can do this by snapping it to the line:

- Click with the
__right__mouse button on the point C. - In the upcoming "context menu" of the point C you chose the item "Snap point to line";
- Click on the line the point C is to be snapped to!

Surely you know that all points with a certain distance from a points A lie on a

Now its your turn to carry out the construction:

You can easily

- Just drag one of the points A or B.

Do all possible points C on the line (ST) have equal distances from A and B?

With the tool "Name object" from the context menu of the constructed straight line you can give this line a name, e.g. "g". When additionally you construct the straight line h through A and B, then you see that g and h are orthogonal. The intersection point M of g and h lies

- The straight line that holds all the points that have equal distances from two given points A and B is called the

- k1 is a circle around A running through B
- k2 is a circle around B running through A
- S and T are the intersection points of k1 and k2
- g is the straight line through S and T

- You are not forced to use the distance of A to B as radius for the circles in the above constructions. But there is a lower limit for the radius. Can you determine the value of this limit?

Is there an upper limit, too?

- The point M also lies halfway between S and T, but this seems not yet clear. Can you complete the drawing to become convinced that this is always true?